The probability density distribution for the power output from arrays of wind turbines and the intermittent nature of wind power

This paper discusses the probability density distribution of the power output from arrays of turbines distributed over different geographical areas. Based on a model of a square array of turbines, estimates are obtained for the reduction in the standard deviation of the power output from the turbine arrays as a function of the area of the square. This simple model is used to derive an estimate for the reduction in the power standard deviation for different lands masses – the UK, Europe and the USA. It is then shown that the probability distribution of the array power output can reasonably be represented by the Weibull distribution which is then used to estimate the percentage of time that the array power output drops below some fraction of the mean power. shown that for the UK, the power output can be expected to drop below 10% of the mean power for about 6% of the time whereas for a European scale grid, this percentage falls to around 0.3% of the time. It is even lower for a land mass like the USA. The implications of these findings for the design of a wind power back-up system are then discussed.